34241 ÷ 4 = 8560 R1
Alright, let's work through the division of 34241 by 4 step by step.

Step 1:
4 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 4

Step 2:
4 goes into 34 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 32 from 34 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 4

Step 3:
4 goes into 22 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 85
Subtract 20 from 22 to get 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 4

Step 4:
4 goes into 24 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 856
Subtract 24 from 24 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 4

Step 5:
4 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 8560
Subtract 0 from 1 to get 1.

The final result is 8560 with a remainder of 1.